If I would rename Ukraine I would name it "Ruthenia", that would include both Ukrainians and Carpathian Rusyns and it's also the historically correct term for Ukraine.
Ruthenia also included today's Belarus. Do you believe Ukraine, Belarus and Rusyns should all be included in this potential state called Ruthenia?
Is it identical situation as we have in Poland, where Silesians and Pommeranians (Kaszuby) are all tribes from same root? I would be willing to rename Poland to Lechia, since it would represent Poles, Silesians and Kuszuby.